Preconditioners for symmetrized Toeplitz and multilevel Toeplitz matrices

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When solving linear systems with nonsymmetric Toeplitz or multilevel Toeplitz matrices using Krylov subspace methods, the coefficient matrix may be symmetrized. The preconditioned MINRES method can then be applied to this symmetrized system, which allows rigorous upper bounds on the number of MINRES iterations to be obtained. However, effective preconditioners for symmetrized (multilevel) Toeplitz matrices are lacking. Here, we propose novel ideal preconditioners, and investigate the spectra of the preconditioned matrices. We show how these preconditioners can be approximated and demonstrate their effectiveness via numerical experiments.
Original languageEnglish
Pages (from-to)870-887
Number of pages18
JournalSIAM Journal on Matrix Analysis and Applications
Issue number3
Publication statusPublished - 16 Jul 2019


  • Toeplitz matrix
  • multilevel Toeplitz matrix
  • symmetrization
  • preconditioning
  • Krylov subspace method


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